Multidimensional data can be collected by means of many different physical processes, for example: images may be collected by a video camera; by radar systems; by sonar systems; by infrared systems; by astronomical observations of star systems; by medical imaging using x-rays with dynamic image recording, magnetic resonance imaging, ultrasound, satellite imaging of the Earth, or by any other technology capable of generating an image of physical objects. The image data may then be analyzed in order to track targets of interest. Tracking is the recursive estimation of a sequence of states that best explains a sequence of observations. The states are specifications of the configuration of a model which is designed to explain the observations.
Modem detectors often return a very large amount of data. For example, a simple video camera produces approximately 30 frames per second (depending on the video protocol) with each frame having approximately 300 pixels horizontally across the image and 200 rows of pixels vertically in the image to yield 60,000 pixels in each image (again the details depending upon the video protocol). It is a very computation intensive process to generate a predicted image for each frame and to compare the predicted image with the actual data in order to refine the state of a model for tracking purposes.
In the event that it is desired to find an image of a face in a video image, there are approximately 60,000 pixels which must be examined for a "face" pattern. Also, a photograph or video image of an automobile running a red light requires extensive analysis in order to read the license number which may be contained in a few pixels of the image. Similarly, analysis of a portion of the Earth by examining an image, for example a television image, from a satellite in orbit around the Earth also will have a correspondingly large amount of data in which a pattern must be sought.
Kalman filter tracking has been successful as a tool for refining the parameters of a model in cases where a probability density function is sufficiently simple. Kalman filters are described by Eli Brookner in the book Tracking and Kalman Filtering Made Easy, published by John Wiley & Sons, Inc., in 1998, all disclosures of which are incorporated herein by reference. However, as data gathered by detectors becomes more complex, and the complex data requires the models to distinguish between ambiguous representations of the data, the simple approach to tracking by Kalman filtering breaks down.
There is needed an improved method for refining the state of a model of objects, where predictions of the model are compared with the large amounts of data produced by modern detectors.